In the greyish-brown(?) corner: The stone giants from the movie, specifically. The ones from the book are not very specifically described. Let's just assume there are no more than three stone giants in this match-up. A bag is like a hole that you can carry with you.

I don't think fire would hurt those things much but smaug might be able to knock their heads off........but if they connected with a huge boulder on smaug they could probably kill him. Smaug has agility and smarts on them I think but it's really hard to say.

As was mentioned, I think Smaug could knock off a stone giant head. In flight, he also could avoid the flying boulders easily. The stone giants seem fairly slow.

However, big questions remain. Where do stone giants fit in the big picture? Can they leave the mountains? Would they attack anyone besides each other? Can they actually die or do they simply take on a new rock form?

i think the Stone Giants would win this one. How would Smaug knock off one of their heads without killing himself and the giants wouldn't be affected by his fire also they could just hide as mountains until he gets close enough to get.

Smaug would be able to knock their heads off, in numerous ways. A well-placed tail-strike for instance, while flying by.

However, from what we have seen, it's still hard to know that would be enough to defeat a stone giant. Knocking it's head off might not be enough. For all we know, they don't need "heads" to keep fighting.

Sure, they can be knocked off the side of the mountain. But that might only prolong the fight rather than end it.

Maybe each one would need to be shattered into pebbles to be stopped permanently?

Smaug can fly and he has only one weakspot. That said, he's an organic being. His endurance is likely to be finite. I expect at some point he needs to take a break from flying and/or fighting and/or breathing fire. With the stone giants, they appear to be made of solid rock. It's hard to say if they ever need to rest.

Plus, even though Smaug has only one weakness for piercing purposes, I would think that his armor would not protect him from bludgeoning attacks, such as from the stone-giants' fists, kicks, or flying boulders.

Smaug can breathe fire and eventually melt rock. But that would take quite a bit of fire, I would think? See my point above about Smaug's endurance. Also, I wonder whether Smaug would have sufficient opportunity to melt any one of them with a concentrated, uninterrupted stream of his fire breath, while the other two are slinging rocks and boulders at him.

If he is breathing a fire attack from the air, wouldn't he have to hover? Or he would have to strafe in a circle while blasting flames at a single target. Either of which would require quite a bit of effort and concentration. While he's busy doing that, doesn't he make himself more vulnerable to attacks from the other two giants?

If he ever lands, even for a moment, he would become vulnerable to close-in attacks and he might even get tackled and wrestled by one if not more than one giant.

If a stone-giant were to hold Smaug down (on level ground, if any) while the other two are there to kick and punch, Smaug's at a great disadvantage.

Additionally, if a stone giant (or two, or three) were to put Smaug into a hold and then fall off the mountain, Smaug would probably not be able to fly to save himself, depending on how strong his wings are. I am sure his wings are very strong but those giants look extremely heavy. Those wings are strong enough to easily lift his own considerable weight, but with the added weight of the giants, I'm doubtful. The resulting fall might hurt Smaug more than the giant, or at least equally so?

So, without more info about the Stone giants' weaknesses and limitations, I would lean toward them over Smaug. A bag is like a hole that you can carry with you.